After debutant Nick Proschwitz, signed on loan from Hull, gave Barnsley a 29th-minute lead against the run of play, Tom Cairney and Rudy Gestede scored to give Blackburn the advantage at the interval.
But the hosts hit back to level midway through the second half when Chris O'Grady scored from the penalty spot after Grant Hanley was controversially adjudged to have fouled Liam Lawrence inside the area.
Wilson said: "I am happy with a point because to go behind against a quality side like Blackburn and fight back like we did...
"It was a controversial decision, I suppose, in Gary's eyes, but in mine we called it straight away.
"If it's a bit of luck on our side, that's the first we've had for a while so I'll take it.
"In the first half they gave us a lesson. They passed us to death at times and we didn't get to grips with it at all.
"They picked up the ball in midfield and played through us. Getting them in at half-time was a bonus from my point of view at only being a goal down.
"We got away with it. We have to be honest. We were more disciplined in the second half and I think we had our fair share of the play and fair share of chances."
Wilson was also pleased with Proschwitz's debut display, saying: "I think you saw exactly what Nick is about.
"He gets into the box all the time. He doesn't need a second glance at whether he's going to take a shot or not.
"He will just pull the trigger. His goal came after a fantastic ball in from Jennings and it was a clinical finish as well. He gets in those areas."
Wilson played down a touchline spat with his opposite number Gary Bowyer, saying: "You can get carried away sometimes and you have to break the ice a bit. It's tense out there.
"Sometimes you just have to lighten it a bit and that's what we did. It was just a nice, gentle conversation."
Blackburn boss Gary Bowyer felt the controversial penalty award overshadowed a good performance from his side.
He said: "Hands up who thought it was a penalty? That says it all.
"The decision is not acceptable. It cannot be. Jordan Rhodes gets flattened in the penalty box. I spoke to the referee but it didn't make me feel any better.
"You should be talking about how well we played, especially in the first half. We were outstanding.
"Their goal came against the run of play but we didn't panic. We just kept playing the way we play and scored two very good goals."